[N,k,chi] = [18,18,Mod(1,18)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(18, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("18.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Newform invariants
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
sage: f.q_expansion() # note that sage often uses an isomorphic number field
For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.
For more information on an embedded modular form you can click on its label.
\( p \) |
Sign
|
\(2\) |
\(-1\) |
\(3\) |
\(-1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5} + 645150 \)
acting on \(S_{18}^{\mathrm{new}}(\Gamma_0(18))\).
$p$ |
$F_p(T)$ |
$2$ |
\( T - 256 \)
|
$3$ |
\( T \)
|
$5$ |
\( T + 645150 \)
|
$7$ |
\( T - 3974432 \)
|
$11$ |
\( T - 500068668 \)
|
$13$ |
\( T + 5425661314 \)
|
$17$ |
\( T - 5466992958 \)
|
$19$ |
\( T + 53889877060 \)
|
$23$ |
\( T + 578906836536 \)
|
$29$ |
\( T - 4619583681690 \)
|
$31$ |
\( T + 6802815567448 \)
|
$37$ |
\( T + 19571909422138 \)
|
$41$ |
\( T + 57213620756922 \)
|
$43$ |
\( T + 24501250225084 \)
|
$47$ |
\( T + 184283998832832 \)
|
$53$ |
\( T - 206542562280354 \)
|
$59$ |
\( T - 418648048246140 \)
|
$61$ |
\( T - 2501287878088382 \)
|
$67$ |
\( T + 145692866050948 \)
|
$71$ |
\( T - 5364313152664248 \)
|
$73$ |
\( T - 3302058927938186 \)
|
$79$ |
\( T - 22\!\cdots\!60 \)
|
$83$ |
\( T + 20\!\cdots\!76 \)
|
$89$ |
\( T - 56\!\cdots\!10 \)
|
$97$ |
\( T + 11\!\cdots\!18 \)
|
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